Prediction-based control of LTI systems with input and output time-varying delays

Abstract

The stability of a prediction-based controller is studied in presence of time-varying delays both in the input and in the output. Thanks to the reduction method and a Lyapunov-Krasovskii analysis, stability conditions are derived. A comparison is also made between the single input delay and single output delay cases. It is shown that this method can be applied to stabilize output delay systems without restriction on the delay rate. The results are illustrated numerically on a double integrator.

Super-Twisting Algorithm-Based Time-Varying Delay Estimation With External Signal

“…they will just be the smallest value that ensures the estimation accuracy. • The stabilization of time-varying delay systems by using the proposed delay estimator and the predictor-based controller (for time-varying delays) [29], [42] will also be considered for future researches.…”

“…Therefore, one can effectively estimate the round-trip delay with the inner loop of s(t) (green loop in Figure 1) that is independent of the control system (black loop in Figure 1). Finally, the remote control system can be stabilized 1 by using the delay estimationĥ(t) and a predictor-based controller [29].…”

A practical online time-varying delay estimation of remote control system based on adaptive super-twisting algorithm

“…Moreover, by comparing with the delay measurement method [15], the proposed method provides better robustness dealing with channel inherent noise and deception attack. The combination of the proposed method and the predictor-based controller [4] for real RCS will be investigated for future work.…”

“…The round-trip delay of the remote control system is estimated only by the estimation loop (s(t) and s(t − h(t))), and the delay estimation is transmitted to the control loop in order to stabilize the system. In [4], the Transmitter stabilization of linear time-invariant (LTI) systems with input and output time-varying delays is studied, the statements in [4, p.27] explain that one can use the round-trip delay (3) to build a predictor-feedback control law.…”

“…However, one must consider the time-delay introduced by the data transmission since the time-delay is a source of instability [2] of the control system. Predictor-feedback (predictor-based controller) [3], [4] is an effective way to compensate the time-delay if the delay value is known. If the remote-control system (RCS) is subject to unknown time-delay, then one can firstly estimate the time-delay and then stabilize the RCS with a predictor-based controller.…”